2006/10/09 by Giuseppe Vitiello, G. Vitiello · 13 citations
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Algebra over a field #Algebraic number #Algebraic structure #Algebraic structures and combinatorial models #Canonical form #Degrees of freedom (physics and chemistry) #Homotopy and Cohomology in Algebraic Topology #Physical system #hep-th
paper · pdf · doi:10.1007/3-540-70859-6_7
published in Lecture notes in physics, 165-205 (Springer Science+Business Media)
arxiv created 2006/10/09 · openalex publication_date 2007/04/13 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
In this report I review some aspects of the algebraic structure of QFT related with the doubling of the degrees of freedom of the system under study. I show how such a doubling is related to the characterizing feature of QFT consisting in the existence of infinitely many unitarily inequivalent representations of the canonical (anti-)commutation relations and how this is described by the q-deformed Hopf algebra. I consider several examples, such as the damped harmonic oscillator, the quantum Brownian motion, thermal field theories, squeezed states, classical-to-quantum relation, and show the analogies, or links, among them arising from the common algebraic structure of the q-deformed Hopf algebra.